strange distort with simple pose on basic cilinder
You might have the origin set wrong. Try selecting the cylinder and pressing the key you have set to search (I have space but you might have to go into edit-preferences and set it to something). Then search for "set origin" and press "origin to geometry". 

My other guess is that there is something wrong with the weights. Try removing the armature and adding in a new one. Select the model and then shift+select the rig and press ctrl+p "with automatic weights".

It also seems like your bones are a bit too far out. Maybe try moving them/scaling them inside the model before applying the weights.